Droplet fragmentation using a mesh

Atomization and spray generation naturally occur around us in a wide variety of situations ranging from drop impacts to bubble bursting. However, controlling this process is key in many applications such as internal combustion engines, gas turbines, and agricultural spraying. Here we show how a drop can be fragmented into thousands of smaller droplets by impacting it onto a mesh. We demonstrate the unexpected possibility to transfer liquid outside the projected impact area of the drop and the existence of a well-defined cone envelope for the resulting spray. Self-similarity of the flow studied at the primary repeating unit—the hole—allows us to predict the global nature of the atomization process: mass transfer and spray geometry. We explain how these elementary units capture the momentum of the flow atop them and how side wall interactions can lead to saturation effects. At the grid level, this translates into surface fraction and hole aspect ratio being governing parameters of the system that can be tuned to control and optimize spray characteristics. As a result of the fragmentation, the momentum exerted on the target is reduced—a major advantage in crop protection and pathogen dispersion prevention under rain. In addition, pesticide drift in agricultural sprays can be controlled by using initially large drops that are subsequently atomized and conically sprayed by a mesh atop the crop. Beyond droplet-substrate interaction, this inexpensive spraying method enhances surface exchange phenomena such as evaporation and has major implications in many applications such as cooling towers or multieffect desalination.

Figure 1

(a) Time lapse of a water drop of radius $R=1.9\mathrm{mm}$ impacting at $V=1.6\mathrm{m}/\mathrm{s}$ onto a nonwetting mesh (mesh number 46 and surface fraction $\varphi =0.48$ corresponding to holes of radius $b=190\mu \mathrm{m}$ and wire diameter $d=170\mu \mathrm{m}$). Time between images 1.5 ms. (b) Chronophotography of droplet impacting on same mesh (represented by the dashed line) as in (a) for speeds $V=1.0$, 1.3, 1.6, 2.7, 4 m/s, increasing from left to right. The time interval between drops before impact (region above the mesh) correspond to 2 ms in all cases. Third chronophotography corresponds to (a).

Figure 2

(a) Chronophotography of a drop ($R=1.1\mathrm{mm}$, $V=2.1\mathrm{m}/\mathrm{s}$) impacting a plate of thickness $h=36\pm 5\mu \mathrm{m}$ pierced with a hole of radius $b=180\pm 10\mu \mathrm{m}$ at an off-centered position $r=0.44R$. We can observe a liquid filament ejected at an angle α. Right top panels show a zoomed sketch of the hole area. Right bottom panel shows a cross-sectional sketch of the hole. (b, c) Angle of ejection $\alpha$ as a function of the normalized off-centering position of the hole $r$/R. Black line shows Eq. (1). Hole radius $b=180\pm 10\mu \mathrm{m}$. (b) Speed $V$ and drop radius $R$ are varied, while plate thickness $h=36\pm 5\mu \mathrm{m}$ is kept constant. (c) Speed $V=2.1\mathrm{m}/\mathrm{s}$ and drop radius $R=1.9\mathrm{mm}$ are kept constant, while plate thickness $h$ is varied. (d) Critical angle ${\alpha }^{*}$ as a function of the hole aspect ratio $h/2b$. Solid line shows Eq. (2) with $A_p/A^{*}=10\%$. Sketches show the real hole aspect ratio for fixed radius $b=180\pm 10\mu \mathrm{m}$ and thickness $h=81$ (red), 160 (light blue), and 525 (blue) μm. The arrow in the sketch shows ${\alpha }^{*}$ and divides the cross section of the hole so that the perturbed area corresponds to 10%.

Figure 3

(a) Transmitted mass percentage as a function of the model prediction [Eq. (3)] for centered holes $r=0\pm 0.2\mathrm{mm}$. Marker type describes hole size $b$: 110 ± 5 μm in circle, 180 ± 10 μm in triangle, 320 ± 10 μm in star. Color describes drop radius $R$: 1.1 mm in red, 1.9 mm in green, 2.8 mm in blue. For a given $R$ and $b$, three speeds were used: 1.4, 2.5, 3.4 m/s. Red line shows equation $y=x$. (b) Side view of drop ($R=1.9\mathrm{mm}$, $V=2.2\mathrm{m}/\mathrm{s}$) impacting on a hole ($b=180\pm 10\mu \mathrm{m}$) with increasing off-centering parameter $r$/$R$: 0, 0.65, 0.95, 1.45 from left to right. Image is taken 1.5 ms after initial touchdown in all cases. White dashed line shows initial drop position and volume. (c) Transmitted mass $m_r$ as a function of the off-centering parameter $r$/$R$ normalized by the center case ${m_{r=}}_0$. $m_r$ ranges over two orders of magnitude: from tens to thousands of μg. Same marker and color definition as in (a). Dashed lines: Vertical shows $r/R=1$ after which rapid decrease of liquid transfer is observed. Horizontal shows maximum transmission happening when $r=0$, the case seen in Fig. 3.

Figure 4

(a) Side (left half) and top (right half) sketch of drop-mesh system. Insets show close-up view detail of geometrical parameters of the grid. (b) Angle of ejection (top row) and transmitted mass percentage (bottom row) for a drop ($R=2.1\mathrm{mm}$) impacting a mesh of constant surface fraction of holes ($\varphi =0.31$ left column) or constant mesh number ($\#=40$, right column) as a function of normalized impacting speed. In the case of mass transmission (bottom), solid lines show best fit following Eq. (5) (the resulting prefactor being $1.1\pm 0.2$). “#” in left panels of (b) is mesh number.

Figure 5

(a) Atomized droplet radius, $r_a$, distribution for drop with velocity $V/V^{*}=3$ impacting a mesh with opening size $b=90$, 150, and 235 μm respectively. (b) Rain of millimetric drops impacting at speed $V=3\mathrm{m}/\mathrm{s}$ directly onto the leaves of a plant (top) or through a mesh [bottom, $\varphi =0.55$, $\mathrm{number}=40$, corresponding to red dots in Fig. 4]. We can observe how in the second case a spray of much finer droplets is generated in situ—typically reducing the momentum of the droplets by a factor of 1000—at the same time that the incoming rain is spread over a larger area.